White version of a product visualisation loosing reflections
White non-metallic surfaces have less shiny reflectivity than black ones of the same smoothness, because white surfaces disperse more light (in multiple directions). Combined with that is the optical illusion that light on a dark object is more visible to the eye than light on a light object. If you already have a white object and you try to make it more white, it's not going to increase as much in visual brightness.

This is how it works in the real world as it works in blender. To force this look with the material you want you can do two things:


You can make the material more metallic by increasing the metallic slider. As you can see that your expected material looks more like aluminium than plastic.
You can increase the specular slider to increase the amount of reflection directly. This slider is there for artistic use like what you seem to be trying.


If you are not at all happy with the workings of the principled shader you can make your own node system by mixing the glossy shader with the diffuse shader and using fresnel (in case of a non metallic object)

Another solution for you might also to increase the contrast of the HDRI by using a gamma node which should make the reflections appear brighter, or use color management to increase the overall gamma of the image.